An 18th-century back-formation from 'donation' — stripping '-tion' from Latin 'donatio' (a giving), from PIE *deh3- (to give).
To give money, goods, or one's time or effort freely, especially to a charity or public institution.
A 19th-century back-formation from 'donation,' which entered English in the 15th century from Old French 'donacion,' from Latin 'dōnātiōnem' (accusative of 'dōnātiō'), the act of giving as a gift, from 'dōnāre' (to give, to present, to bestow as a gift), from 'dōnum' (a gift), from PIE *deh₃- (to give). The PIE root *deh₃- is one of the core Indo-European giving-words: Sanskrit 'dā-' (to give), 'dānam' (gift), Greek 'dōron' (gift), 'didōmi' (I give), Old Church Slavonic 'dati' (to give), English 'date' (something given, a fixed point — from Latin 'data', given). Latin built richly on this root
The verb 'donate' is a back-formation — a word created by removing what looks like a suffix from an existing word. English speakers had 'donation' (from Latin) for three centuries before someone assumed that if a 'donation' is the noun, 'donate' must be the verb. This reverse-engineering of the verb from the noun